Question

The cone shown has a volume of 12 pi inches find the volume of a cylinder with the same base and height as the cone

Answer 1

The volume of a cone is (1/3)pi r^2 and of a cylinder it is just pi r^2. So the volume of the cylinder will be 3 times that of the cone with the same base and height. So V_cylinder = 36 pi inches^3

Remember: inches is a unit of length in 1D. For 3D volume use inches^3

Answer 2

$\bf \begin{array}{llll} \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h} \\\\\\ \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{1}{3}(\pi r^2 h)} \end{array}\qquad \qquad \begin{cases} r=radius\\ h=height \end{cases}$

so, if we notice those two volumes, the cone's volume is really 1/3 that of the cylinder's, with the same "r" and "h", namely, the cylinder's volume is 3 times as large.

we know the cone has a volume of 12π, so the cylinder's volume must be 3 times as much, 3*12π = 36π.